Research Methodology - Dr. Krishan K. Pandey

256 Research Methodology
ANALYSIS OF VARIANCE (ANOVA)
11
Analysis of Variance
and Co-variance
Analysis of variance (abbreviated as ANOVA) is an extremely useful technique concerning researches
in the fields of economics, biology, education, psychology, sociology, business/industry and in researches
of several other disciplines. This technique is used when multiple sample cases are involved. As
stated earlier, the significance of the difference between the means of two samples can be judged
through either z-test or the t-test, but the difficulty arises when we happen to examine the significance
of the difference amongst more than two sample means at the same time. The ANOVA technique
enables us to perform this simultaneous test and as such is considered to be an important tool of
analysis in the hands of a researcher. Using this technique, one can draw inferences about whether
the samples have been drawn from populations having the same mean.
The ANOVA technique is important in the context of all those situations where we want to
compare more than two populations such as in comparing the yield of crop from several varieties of
seeds, the gasoline mileage of four automobiles, the smoking habits of five groups of university
students and so on. In such circumstances one generally does not want to consider all possible
combinations of two populations at a time for that would require a great number of tests before we
would be able to arrive at a decision. This would also consume lot of time and money, and even then
certain relationships may be left unidentified (particularly the interaction effects). Therefore, one
quite often utilizes the ANOVA technique and through it investigates the differences among the
means of all the populations simultaneously.
WHAT IS ANOVA?
Professor R.A. Fisher was the first man to use the term ‘Variance’ * and, in fact, it was he who
developed a very elaborate theory concerning ANOVA, explaining its usefulness in practical field.
* Variance is an important statistical measure and is described as the mean of the squares of deviations taken from the
mean of the given series of data. It is a frequently used measure of variation. Its squareroot is known as standard deviation,
i.e., Standard deviation = Variance.